The `N_(2)O_(4)//NO_(2(g))` equilibrium is endothermic as shown below:
`underset(Colourl es)(N_(2)O_(4(g)))hArrunderset(Dark brown)(2NO_(2(g)))`, (`DeltaH=+ve`)
The equilibrium is attained in a container having movable piston by taking `1 mol e` of `N_(2)O_(4(g))` at `50^(@)C` and `1 atm` pressure. At equilibrium, relative molecular mass of the mixture is `65.7`.
The equilibrium constant for the given reaction is:

Options

A. `2.9 mol dm^(3)`
B. `0.29 mol dm^(3)`
C. `0.029 mol dm^(3)`
D. `0.0029 mol dm^(3)`

Explanation

Total mole at equilibrium
`=1+alpha=1+0.4=1.4`
`:. V=(nRT)/(P)=(1.4xx0.0821xx323)/(1)`
`=37.13 dm^(3)`
`:. K_(c)=((2alpha)^(2))/(V(1-alpha))=((2xx0.4)^(2))/(37.13xx0.6)`
`=0.029 mol dm^(3)`